Special Unitary Group of degree n

URI: https://gptkb.org/entity/Special_Unitary_Group_of_degree_n
GPTKB entity
Statements (50)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkbp:actsOn complex n-dimensional vector space
gptkbp:alsoKnownAs gptkb:SU(n)
gptkbp:application standard model of particle physics
gptkbp:centralTo cyclic group of order n
Z_n
gptkbp:compact compact
gptkbp:connectedness connected
gptkbp:definedIn group of n x n unitary matrices with determinant 1
gptkbp:dimensions n^2 - 1
gptkbp:field complex numbers
gptkbp:firstChernClass 0
gptkbp:firstHomotopyGroup Z_n
gptkbp:fundamentalGroup Z_n
gptkbp:generation traceless Hermitian matrices
gptkbp:hasSpecialCase SU(2) is isomorphic to the group of unit quaternions
SU(1) is the trivial group
SU(3) is important in quantum chromodynamics
gptkbp:hasSubgroup gptkb:unitary_group_U(n)
gptkbp:homologyGroup H_1(SU(n), Z) = 0
gptkbp:homotopyGroup π_1(SU(n)) = Z_n
https://www.w3.org/2000/01/rdf-schema#label Special Unitary Group of degree n
gptkbp:identityElement identity matrix
gptkbp:irreducibleRepresentations classified by highest weights
gptkbp:isA gptkb:group_of_people
gptkb:Lie_group
gptkb:matrix_Lie_group
simple group
non-abelian group
compact group
connected group
gptkbp:isSimple n ≥ 2
gptkbp:Lie_algebra su(n)
gptkbp:matrixCondition U†U = I, det(U) = 1
gptkbp:maximalTorus (n-1)-dimensional
gptkbp:notation gptkb:SU(n)
gptkbp:order infinite
gptkbp:rank n-1
gptkbp:realDimension n^2 - 1
gptkbp:relatedTo gptkb:special_linear_group_SL(n,_C)
gptkb:unitary_group_U(n)
orthogonal group
projective special unitary group PSU(n)
gptkbp:usedIn gptkb:gauge_theory
differential geometry
particle physics
quantum mechanics
representation theory
gptkbp:bfsParent gptkb:SU(n)
gptkbp:bfsLayer 6